A complex hollow part surface area calculation method combined with computer vision

Abstract

This invention relates to the field of industrial measurement and testing technology, and discloses a method for calculating the surface area of ​​complex hollow parts using computer vision. For rotationally symmetric hollow parts, a polar reference system is established, consisting of a Cartesian coordinate system and a polar coordinate system aligned with the main rotation axis. Boundary distances are acquired in the polar angle and height directions, and a polar boundary matrix is ​​constructed. Micro-elements are divided on the polar mesh, and local surface areas are calculated. The variance of the measurement data is calculated, and unstable positions are corrected. Based on updated data, hollow areas are identified, and a mask matrix is ​​constructed to correct local surface areas. The final total surface area is obtained by summing the data, and the area ratio of each layer is statistically analyzed according to height. Through these steps, the true surface of the part is accurately reflected under a unified reference system, hollow areas are automatically eliminated, posture errors and noise are reduced, and a stable and reliable exposed surface area and area distribution in the height direction are obtained, providing a basis for heat transfer, coating, and structural optimization.

Description

Technical Field

[0001] This invention relates to the field of industrial measurement and testing technology, specifically a method for calculating the surface area of ​​complex hollow parts using computer vision. Background Technology

[0002] In the field of dimensional inspection and quality assessment of complex structural components, the surface area of ​​rotationally symmetric hollow parts (such as complex heat dissipation structures, filter components, and special shells) is often directly related to key indicators such as heat transfer efficiency, coating amount, and surface treatment cost. In existing technologies, the surface area is typically calculated by a CAD system after modeling the part using 3D modeling software, or by acquiring point cloud data using 3D scanning equipment and then performing mesh reconstruction and surface area calculation using specialized software. In some production sites, the surface area is also estimated using simple geometric relationships on only a few cross-sections.

[0003] However, the aforementioned existing technologies have several limitations when used for complex hollowed-out parts. Firstly, calculations based on ideal CAD models or regular geometric assumptions struggle to reflect actual dimensional deviations and local deformations after machining. Furthermore, it's difficult to establish a unified reference system consistent with the part's rotation axis for the on-site clamping posture, leading to discrepancies between the surface area results and the actual physical state. Secondly, the large volume of point cloud data acquired through 3D scanning and the complex processing chain mean that distinguishing between hollowed-out and solid areas often relies on manually setting regions or selecting boundaries. This makes it difficult to form ordered measurement data corresponding one-to-one with polar angles and height layers within the polar coordinate domain around the rotation axis, and the subsequent processes of local surface area integration and overall accumulation are not standardized enough. Moreover, existing measurement methods often handle the stability of multiple distance measurement data and suppress noise in a coarse manner, typically relying on simple averaging or outlier removal without specifically interpolating unstable measurement locations in the polar angle and height directions using discrete gradient relationships. This easily amplifies the impact of measurement variance on the surface area results. For complex hollow structures inside hollow parts, existing technologies lack a mechanism for automatically identifying hollow areas based on radial distance variation patterns. This makes it difficult to mask hollow areas within a unified data matrix and effectively remove them from the surface area integral. Furthermore, existing technologies often use the overall value of the inner or outer surface area as the calculation target, rarely providing the layered surface area and its proportion along the height direction. This fails to intuitively characterize the surface area distribution of the hollow structure in the height direction, limiting the ability to subsequently optimize heat transfer, flow, or coating processes.

[0004] Therefore, this case aims to propose a method for calculating the surface area of ​​complex hollow parts by combining computer vision. For rotationally symmetric complex hollow parts, a polar domain reference system combining polar coordinates and height layers is established around the rotation axis of the real part. Boundary distance data is obtained in this reference system using a regular grid, and the surface of the real part is mapped to a discrete polar domain function. Then, through a complete set of computer vision and numerical processing procedures such as infinitesimal patch integration, variance suppression, hollow masking, and height layer statistics, the external surface area and distribution characteristics are obtained, which are both consistent with the actual processing state and can be analyzed in layers. Summary of the Invention

[0005] This invention provides a method for calculating the surface area of ​​complex hollowed-out parts by combining computer vision, which helps to solve the problems mentioned in the background art.

[0006] This invention provides the following technical solution: a method for calculating the surface area of ​​complex hollowed-out parts using computer vision, comprising:

[0007] The scene is initialized for the rotationally symmetric hollow part, and a polar reference system consisting of a plane rectangular coordinate system and a polar coordinate system is established around the main rotation axis and the geometric origin;

[0008] In the polar reference frame, the boundary distance measurement results distributed along the polar angle direction and the height layer are obtained, and a polar boundary data matrix covering each polar angle direction and each height layer is constructed based on these boundary distance measurement results;

[0009] In the polar domain boundary data matrix, micro-element cells are divided according to the grid of polar angle and height. The radial distance difference between adjacent positions is obtained for each micro-element cell to construct micro-element patch data and corresponding gradient information.

[0010] Based on the data of each micro-element patch and gradient information, the local surface areas on the mesh are accumulated to obtain the original total surface area of ​​the outer surface of the complex hollow part.

[0011] The variance of multiple measurements at each measurement location is calculated. Based on the variance distribution, adjacency interpolation correction is performed on unstable locations, the boundary distance data is updated, and the corresponding local surface area is reacquired.

[0012] Based on the updated boundary distance data, the distance difference between polar angle directions is analyzed at each height layer to identify hollow areas and solid areas. A mask matrix is ​​constructed and applied to the local surface area data to obtain the corrected local surface area at each polar angle direction and at each height layer combination position, and a corrected local surface area dataset containing the corrected local surface area at all combination positions is formed.

[0013] Unit conversion and scale unification are performed on the modified local surface area dataset, and the modified local surface area of ​​all micro-element units is accumulated to obtain the final total surface area result of the outer surface of the complex hollow part.

[0014] The local surface area is cumulatively corrected according to the height layer, and the layer surface area and the ratio of the layer surface area of ​​each height layer are obtained to form the surface area distribution feature of the hollow part along the height direction.

[0015] Optionally, the scene initialization of the rotationally symmetric hollow part, establishing a polar reference system composed of a Cartesian coordinate system and a polar coordinate system around the main rotation axis and the geometric origin, specifically includes:

[0016] The rotationally symmetric hollow part to be inspected is clamped on the rotary worktable by a mechanical fixing device, so that the main rotation axis of the hollow part is kept vertical and orthogonal to the horizontal working plane, and the intersection of the main rotation axis and the plane of the rotary worktable is set as the geometric origin.

[0017] Establish a Cartesian coordinate system in the horizontal working plane, set the coordinates of the geometric origin in the Cartesian coordinate system as the zero point coordinates, point the positive direction of the first coordinate axis to the reference direction selected on site, and set the positive direction of the second coordinate axis relative to the first coordinate axis according to the right-hand rule.

[0018] Based on the Cartesian coordinate system, a two-dimensional polar coordinate system is established with the geometric origin as the pole. Multiple polar directions are divided within a circumference angle according to the same angular interval. Discrete indices are assigned to each polar direction, and the correspondence between each polar direction and the Cartesian coordinate system is recorded.

[0019] The lowest and highest measurement height positions of the part under test are obtained along the main rotation axis, forming an axial measurement interval between them, and the coordinates of the lowest and highest measurement heights are recorded respectively.

[0020] Within the axial measurement range, multiple height layers are divided according to the same axial spacing. A height layer index is assigned to each height layer. The axial height coordinates corresponding to each height layer are calculated based on the lowest measured height coordinates and the fixed axial spacing, so that the axial spacing between any two adjacent height layers remains consistent.

[0021] On the horizontal section corresponding to each height layer, laser ranging units are arranged around the geometric origin along each polar angle direction, with the same number of units as the polar angle direction, so that the ranging beam of each laser ranging unit points from the geometric origin along the corresponding polar angle direction to the outer surface of the hollow part.

[0022] Each laser ranging unit is controlled to perform radial scanning on the surface of the hollowed-out part at its specified height layer and polar angle direction, and the distance from the geometric origin to the surface boundary is recorded as the raw ranging data to complete the scene initialization and polar domain reference system establishment.

[0023] Optionally, the step of obtaining boundary distance measurements along the polar angle direction and altitude layer in the polar reference frame, and constructing a polar domain boundary data matrix covering each polar angle direction and altitude layer based on these boundary distance measurements, specifically includes:

[0024] At each combination position of polar angle and height layer, the corresponding laser ranging unit is controlled to perform multiple radial ranging operations according to the preset number of repetitions. The ranging result from the geometric origin to the boundary of the hollow part surface is recorded as the boundary distance measurement data of the corresponding combination position of polar angle and height layer.

[0025] For each combination position of polar angle direction and height layer, the arithmetic mean of multiple boundary distance measurement data recorded for the corresponding polar angle direction and height layer combination position is calculated to obtain the effective boundary distance of the corresponding polar angle direction and height layer combination position. The effective boundary distance is regarded as the average radial distance from the geometric origin to the boundary of the surface of the hollow part at the corresponding polar angle direction and height layer position.

[0026] Within the discrete two-dimensional domain spanned by all polar angle direction indices and height layer indices, a polar domain boundary data matrix is ​​established according to the polar angle direction index and height layer index. Each matrix cell corresponds one-to-one with a combination position of polar angle direction and height layer. The effective boundary distance of each combination position of polar angle direction and height layer is written into the corresponding matrix cell to form the discrete boundary function value in the polar domain boundary data matrix.

[0027] Optionally, the step of dividing the polar boundary data matrix into micro-element cells according to the grid of polar angle and height, obtaining the radial distance difference between adjacent positions for each micro-element cell, and constructing micro-element patch data and corresponding gradient information specifically includes:

[0028] In the polar domain boundary data matrix, on the discrete grid formed by the polar angle direction index and the height layer index, for each height layer other than the highest height layer, two adjacent polar angle directions and the corresponding polar angle direction between the corresponding height layer and the height layer above it are selected in the corresponding height layer to form a micro-element containing four discrete positions, so that each micro-element is limited by the four effective boundary distances of the same pair of polar angle directions on two adjacent height layers.

[0029] Set a fixed angle interval in the polar angle direction, set the polar angle difference between any two adjacent polar angle directions to the same angle value, and when the polar angle index reaches the maximum value, regard the polar angle direction corresponding to the maximum value of the polar angle index and the polar angle direction corresponding to the minimum value of the polar angle index as adjacent to each other, forming a periodic connection of polar angle directions.

[0030] For each micro-element, the angular gradient is calculated in the polar angle direction. The ratio of the difference between the effective boundary distances of two adjacent polar angle directions at the same height position within the same height layer to the fixed angular interval in the polar angle direction is used as the discrete gradient along the polar angle direction at the corresponding height position within the corresponding height layer.

[0031] For each micro-element, the height gradient is calculated in the height direction. The ratio of the difference between the effective boundary distances of two adjacent height layers in the same polar angle direction to the fixed axial spacing between adjacent height layers is used as the discrete gradient of the corresponding height position in the same polar angle direction along the height direction.

[0032] For each micro-element, first sum the square of the effective boundary distance, the square of the angular gradient, and the square of the product of the effective boundary distance and the height gradient within the micro-element. Take the square root of the summation result to obtain the surface scale factor of the corresponding micro-element. Then multiply the surface scale factor by the fixed angular interval in the polar direction and the fixed axial spacing in the height direction to obtain the local surface area of ​​the corresponding micro-element, forming local micro-element patch data.

[0033] Optionally, the step of accumulating the local surface areas on the mesh based on the data of each micro-element patch and gradient information to obtain the original total surface area of ​​the outer surface of the complex hollowed-out part specifically includes:

[0034] By calling the local micro-element patch data, the local surface area of ​​all micro-element units in the discrete grid composed of polar angle direction index and height layer index is accumulated to obtain the original total surface area of ​​the outer surface of the complex hollow part.

[0035] During the local surface accumulation process, a periodic connection relationship is adopted in the polar angle direction, and the maximum polar angle index position is regarded as adjacent to the minimum polar angle index position. In the height direction, an index range from the lowest height layer to the second to last height layer is adopted.

[0036] Optionally, the step of calculating the variance of multiple measurement data at each measurement location, performing adjacency interpolation correction on unstable locations based on the variance distribution, updating boundary distance data, and re-acquiring the corresponding local surface area specifically includes:

[0037] For each combination of polar angle direction and height layer, read multiple boundary distance measurement data and effective boundary distance of the corresponding polar angle direction and height layer combination location. Squat the difference between each boundary distance measurement data and the corresponding effective boundary distance, sum them, and then divide by the number of distance measurement repetitions of the corresponding polar angle direction and height layer combination location to obtain the radial measurement variance of the corresponding polar angle direction and height layer combination location.

[0038] At all combinations of polar angles and all height layers, the radial measurement variances at each combination are calculated using an arithmetic mean to obtain the global average variance.

[0039] For each polar angle direction and its combination with all altitude layers except the highest altitude layer, the radial measurement variance of the corresponding polar angle direction and its combination with the global average variance is compared. When the radial measurement variance is greater than the global average variance, the effective boundary distances of two adjacent polar angle direction positions within the same altitude layer are selected, and the arithmetic mean of these two effective boundary distances is calculated. This arithmetic mean is then entered into the corresponding polar angle direction and its combination with the corresponding altitude layer as the updated boundary distance. When the radial measurement variance is not greater than the global average variance, the original effective boundary distances of the corresponding polar angle direction and its combination with the corresponding altitude layer remain unchanged.

[0040] After updating the boundary distances of all combined locations, the angular gradient and height gradient of each combined location are recalculated based on the updated boundary distance data and the boundary distances of adjacent locations. The local surface area of ​​each micro-element is then re-obtained according to the same surface area approximation calculation relationship as when calculating the gradient, forming local micro-element patch data after variance suppression.

[0041] Optionally, based on the updated boundary distance data, the distance difference between polar angle directions is analyzed at each height layer to identify hollow areas and solid areas. A mask matrix is ​​constructed and applied to the local surface area data to obtain the corrected local surface area at each polar angle direction and each height layer combination location. This forms a corrected local surface area dataset containing the corrected local surface area at all combination locations, specifically including:

[0042] For each altitude layer other than the highest altitude layer, the effective boundary distance of each polar angle direction is read in the order of polar angle index within the corresponding altitude layer. For any two adjacent polar angle directions, the absolute value of the difference between the effective boundary distances of these two polar angle directions is calculated within the same altitude layer. The obtained absolute difference is used as the radial difference of the corresponding polar angle direction pair within the corresponding altitude layer. When the polar angle index reaches its maximum value, the polar angle direction corresponding to the maximum value of the polar angle index and the polar angle direction corresponding to the minimum value of the polar angle index are regarded as adjacent and participate in the radial difference calculation.

[0043] For each height layer except the highest height layer, collect the radial differences of all polar angle pairs within the corresponding height layer. Sort these radial differences in ascending order of value. When the number of radial differences is odd, select the radial difference at the middle position after sorting as the median radial difference of the corresponding height layer. When the number of radial differences is even, select the arithmetic mean of the radial differences at the two middle positions after sorting as the median radial difference of the corresponding height layer. Set the median radial difference as the cutout detection threshold of the corresponding height layer.

[0044] For each polar angle direction and the combination position of each height layer except the highest height layer, read the radial difference value related to the corresponding polar angle direction within the corresponding height layer. Compare the read radial difference value with the hollow detection threshold of the corresponding height layer. When the radial difference value is greater than the hollow detection threshold, mark the combination position of the corresponding polar angle direction and the corresponding height layer as a hollow area and assign a value of zero in the mask matrix. When the radial difference value is not greater than the hollow detection threshold, mark the combination position of the corresponding polar angle direction and the corresponding height layer as a solid surface area and assign a value of one in the mask matrix.

[0045] For each polar angle direction and the combination position of each height layer except the highest height layer, the value in the mask matrix is ​​multiplied by the local surface area corresponding to the combination position of the corresponding polar angle direction and the corresponding height layer to obtain the corrected local surface area after considering the suppression of the hollow area, and a corrected local surface area dataset containing the corrected local surface area of ​​all combination positions is constructed.

[0046] Optionally, the step of performing unit conversion and scale unification on the corrected local surface area dataset, and accumulating the corrected local surface areas of all micro-element units to obtain the final total surface area result of the outer surface of the complex hollowed-out part, specifically includes:

[0047] Read the modified local surface area dataset, accumulate the modified local surface area of ​​all combined positions formed by polar angle direction index and height layer index, and obtain the initial value of the total surface area of ​​the outer surface of the complex hollow part.

[0048] Based on the conversion relationship between the area unit of the measurement system and the expected output area unit, the initial value of the total surface area is converted to obtain the final total surface area result expressed in the expected output area unit, and the final total surface area result is stored or output.

[0049] Optionally, the step of cumulatively correcting the local surface area according to the height layer to obtain the layered surface area and the layered surface area ratio of each height layer, forming the surface area distribution feature of the hollow part along the height direction, specifically includes:

[0050] For each height layer except the highest height layer, the corrected local surface area of ​​all polar angle directions within the corresponding height layer is accumulated to obtain the layered surface area of ​​the corresponding height layer. The layered surface areas of all height layers are arranged in order of height layer index to form a surface area sequence along the height direction.

[0051] If the final total surface area is greater than zero, the ratio of the layered surface area of ​​each height layer to the final total surface area is calculated to obtain the proportion of the layered surface area of ​​each height layer in the final total surface area. If the final total surface area is equal to zero, the proportion of the layered surface area of ​​all height layers is uniformly set to zero.

[0052] The final total surface area is used as the overall surface area feature of the complex hollowed-out part, and the surface area sequence in the height direction and the corresponding layered surface area ratio are used as the surface integral distribution feature of the complex hollowed-out part along the height direction, forming a quantitative characterization result of the complex hollowed-out structure.

[0053] The present invention has the following beneficial effects:

[0054] 1. First, a mechanical fixture is used to ensure the main rotation axis of the part is strictly perpendicular to the working plane. The intersection of the rotation axis and the worktable is clearly defined as the geometric origin. Then, a Cartesian coordinate system is established on the working plane, and a polar coordinate system with the geometric origin as the pole is established on this basis. At the same time, equidistant height layers are divided along the rotation axis, and laser ranging units are arranged at equal angular intervals on the cross section of each height layer. This scheme, through strong constraint clamping and the joint construction of dual coordinate systems, establishes a one-to-one correspondence between polar angle, height layer, and ranging direction. This provides a rigorous geometric foundation for subsequent construction of data matrices in the polar domain, local gradient calculation, and hollow detection. It reduces the impact of coordinate registration errors and attitude errors on the surface area results, and makes the sampling points naturally distributed in a regular grid, reducing the complexity of subsequent interpolation and resampling.

[0055] 2. The scheme first performs repeated distance measurements at each combination of polar angle and altitude layer. The average of these repeated measurements is used as the effective boundary distance for that location. Then, a complete boundary data matrix is ​​constructed in the polar domain, using the polar angle index and altitude layer index as rows and columns. This elevates the originally scattered and noisy radial distance measurement points into function values ​​defined on a discrete grid of polar angle and altitude layers. The ranging error is explicitly modeled using repeated measurement averaging, while the matrix structure fixes each measurement location on a regular topology. This scheme, through the polar domain matrix form, allows the boundary distances at any polar angle and altitude layer location to be directly indexed, facilitating subsequent calculations of differences and gradients along both the polar angle and altitude directions. On one hand, repeated measurement averaging improves the stability of single-point distance data; on the other hand, the structured representation of the polar domain matrix provides high-quality input for subsequent local area calculations and cutout determination, reducing fluctuations in area calculations caused by measurement noise and data irregularities.

[0056] 3. The scheme uses four discrete points from adjacent polar angles and adjacent height layers to form polar surface micro-element units on the polar boundary data matrix. Each micro-element is considered a local approximation of the real surface, and the area of ​​the micro-element surface is approximated by the radial distance value and the discrete gradients along the polar angle and height directions. This scheme explicitly considers the rate of change of the surface in the polar angle and height directions by using a combination of radial distance and directional gradients. The surface of complex hollow parts is regarded as a function that changes slowly in the polar domain, and its local area is determined by the radial scale and the changes in the two directions. It makes full use of the geometric laws of rotationally symmetric parts in polar coordinates, making the local area approximation more consistent with the actual surface undulations. The micro-element division rules are controllable, and the discrete density of the polar angle and height layers can be adjusted according to the processing accuracy and surface complexity. The gradient participates in the area calculation, which can better reflect the contribution of surface slope and local bending to the area, making the overall surface area result more accurate and reliable.

[0057] 4. The scheme, while ensuring periodic connections in the polar angle direction and consistency with the height layer index range, accumulates the local areas of all polar domain micro-element units to obtain the original total surface area of ​​the complex hollowed-out part. The global integration in this scheme is based on real measurement data, does not rely on the perfection of the theoretical model, and does not require fitting the point cloud into a continuous surface before calculation. First, periodic connections in the polar angle direction ensure that gaps between the first and last polar angles are correctly calculated, preventing area loss due to index truncation. Second, micro-elements are constructed only between adjacent height layers in the height direction, strictly controlling the physical height range corresponding to the integration region. This ensures that the integration result geometrically completely covers the entire outer surface, while avoiding duplicate and omission statistics. The resulting original surface area faithfully reflects the measurement data and maintains strict numerical consistency, providing a reliable starting point for subsequent noise suppression and hollowed-out region removal.

[0058] 5. The scheme first constructs the variance of each polar angle and height layer combination position based on repeated ranging results at the same location. Then, it calculates the global average of the variances of all positions, using this as the baseline for the measurement noise level. For high-fluctuation positions with variances greater than the baseline, it replaces the original distance values ​​with adjacent interpolation in the direction of the adjacent polar angle. Based on the updated distance data, it recalculates the discrete gradient and the area of ​​the infinitesimal element. Using the global average variance as a reference, it distinguishes local abnormal fluctuation regions and uses the correlation between adjacent positions at the same height layer for interpolation correction. This avoids excessively smoothing out the details of the entire surface while specifically eliminating ranging jitter caused by reflections, occlusions, or local defects. It reduces the amplification effect of local measurement instability on the global surface area, making the final area result more noise-resistant. At the same time, it maintains the smoothness and continuity of the polar domain data, without sacrificing real surface features like simple filtering, which is particularly important for complex hollow parts with small steps or holes on the surface.

[0059] 6. The scheme calculates the radial difference between adjacent polar angle directions within each height layer. By sorting these differences and taking the median, a radial difference threshold for that height layer is constructed. Radial difference changes exceeding the threshold are identified as jumps through the hollowed-out region. Based on this, a mask matrix marking the solid and hollowed-out regions is formed in the polar domain. This mask is then applied to the local area, preventing the local area corresponding to the hollowed-out region from being included in the outer surface area calculation. This scheme automatically identifies hollowed-out structures based entirely on the variation pattern of the measured radial data itself, using the median threshold to suppress interference from individual abnormal differences. It can automatically distinguish between hollowed-out and solid structures in the polar domain data without requiring a complete internal structural model beforehand, avoiding the miscalculation of internal cavities, channels, and other non-exposed surfaces in the surface area calculation. Furthermore, by using independent thresholds at different height layers, hollowed-out structures at different heights can be adaptively identified, thereby improving the accuracy of surface area calculation for complex structural components.

[0060] 7. Based on the corrected local area with applied masking, the scheme accumulates the corrected local areas at all combinations of polar angles and height layers to obtain the final total surface area of ​​the hollowed-out part. Then, unit conversion and scale standardization are performed according to engineering needs. Although this step may seem like just a numerical summary and unit processing, its innovative significance lies in concentrating the results of noise reduction, hollowing out, and geometric integrity maintenance from previous steps into a single, directly usable engineering indicator, forming a comparable and traceable surface area result. Each part of the final area value in this scheme can be traced back to a specific polar angle, height layer, and micro-element, possessing high interpretability. This allows the measurement results to be directly linked to process design, cost accounting, and quality judgment standards, meeting the requirements of engineering applications for units and accuracy while maintaining the transparency of the data source, facilitating layer-by-layer investigation and correction when anomalies are discovered.

[0061] 8. The scheme accumulates the corrected local surface areas in all polar angular directions within each height layer to obtain the layered surface area of ​​that height layer. The layered surface areas of all height layers are then arranged in height order to form a surface area sequence along the height direction. If the total surface area is greater than zero, the proportion of the layered surface area in each height layer to the total surface area is further calculated to obtain a layered surface area ratio sequence. The total surface area is used as the overall feature quantity, while the layered surface areas and their ratios are used as distribution features along the height direction. This algorithm provides longitudinally resolved area distribution information for complex hollowed-out parts, reflecting the surface complexity and the concentration of hollowed-out structures in different height ranges. It allows for refined optimization of the performance analysis of products such as heat exchangers and coated parts by incorporating surface area distribution along the height direction. For example, it identifies which height ranges have dense surface areas and may become key areas for heat exchange or wear, thereby guiding local structural improvements or local reinforcement treatments. This achieves a leap from overall quantity to distribution characteristics, expanding the engineering value of surface area calculation results. Attached Figure Description

[0062] Figure 1 This is a schematic diagram of the process of the present invention. Detailed Implementation

[0063] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0064] Example, refer to Figure 1 A method for calculating the surface area of ​​complex hollowed-out parts using computer vision, comprising:

[0065] The scene is initialized for the rotationally symmetric hollow part, and a polar reference system consisting of a plane rectangular coordinate system and a polar coordinate system is established around the main rotation axis and the geometric origin;

[0066] In the polar reference frame, the boundary distance measurement results distributed along the polar angle direction and the height layer are obtained, and a polar boundary data matrix covering each polar angle direction and each height layer is constructed based on these boundary distance measurement results;

[0067] In the polar domain boundary data matrix, micro-element cells are divided according to the grid of polar angle and height. The radial distance difference between adjacent positions is obtained for each micro-element cell to construct micro-element patch data and corresponding gradient information.

[0068] Based on the data of each micro-element patch and gradient information, the local surface areas on the mesh are accumulated to obtain the original total surface area of ​​the outer surface of the complex hollow part.

[0069] The variance of multiple measurements at each measurement location is calculated. Based on the variance distribution, adjacency interpolation correction is performed on unstable locations, the boundary distance data is updated, and the corresponding local surface area is reacquired.

[0070] Based on the updated boundary distance data, the distance difference between polar angle directions is analyzed at each height layer to identify hollow areas and solid areas. A mask matrix is ​​constructed and applied to the local surface area data to obtain the corrected local surface area at each polar angle direction and at each height layer combination position, and a corrected local surface area dataset containing the corrected local surface area at all combination positions is formed.

[0071] Unit conversion and scale unification are performed on the modified local surface area dataset, and the modified local surface area of ​​all micro-element units is accumulated to obtain the final total surface area result of the outer surface of the complex hollow part.

[0072] The local surface area is cumulatively corrected according to the height layer, and the layer surface area and the ratio of the layer surface area of ​​each height layer are obtained to form the surface area distribution feature of the hollow part along the height direction.

[0073] By sequentially setting scene initialization and coordinate system establishment, obtaining the boundary distances of polar angle and height direction and constructing a polar domain data matrix, dividing the polar domain mesh into micro-elements and calculating the local surface area, using multiple measurement variances to interpolate and correct unstable positions, using a mask matrix to distinguish between hollow areas and solid areas and correcting the local area, accumulating the corrected local areas to obtain the final total surface area, and performing layered area and proportion statistics according to height layers, this method solves the technical problems of traditional methods, such as difficulty in accurately describing the actual part surface under a unified geometric reference system, difficulty in automatically removing hollow areas in area calculation, and difficulty in evaluating the distribution of surface area in the height direction. The advantages of this holistic approach are as follows: it binds surface area calculations to a polar reference system aligned with the part's axis from the outset, and the measurement data is organized into a regular polar angle and height grid, which facilitates subsequent numerical processing and reduces attitude errors; through variance-driven interpolation correction and mask matrix removal of hollow areas, the final area result reflects a more realistic and stable exposed surface; and through height-layered accumulation and proportional calculation, it provides engineers with area distribution information in the height direction, which can be used for regional design in subsequent heat transfer, coating, or structural optimization, rather than just a single overall area value.

[0074] The process of initializing the scene for the rotationally symmetric hollowed-out component, and establishing a polar reference system composed of a Cartesian coordinate system and a polar coordinate system around the main rotation axis and the geometric origin, specifically includes:

[0075] The rotationally symmetric hollow part to be inspected is clamped on the rotary worktable by a mechanical fixing device, so that the main rotation axis of the hollow part is kept vertical and orthogonal to the horizontal working plane, and the intersection of the main rotation axis and the plane of the rotary worktable is set as the geometric origin.

[0076] Establish a Cartesian coordinate system in the horizontal working plane, set the coordinates of the geometric origin in the Cartesian coordinate system as the zero point coordinates, point the positive direction of the first coordinate axis to the reference direction selected on site, and set the positive direction of the second coordinate axis relative to the first coordinate axis according to the right-hand rule.

[0077] Based on the Cartesian coordinate system, a two-dimensional polar coordinate system is established with the geometric origin as the pole. Multiple polar directions are divided within a circumference angle according to the same angular interval. Discrete indices are assigned to each polar direction, and the correspondence between each polar direction and the Cartesian coordinate system is recorded.

[0078] The lowest and highest measurement height positions of the part under test are obtained along the main rotation axis, forming an axial measurement interval between them, and the coordinates of the lowest and highest measurement heights are recorded respectively.

[0079] Within the axial measurement range, multiple height layers are divided according to the same axial spacing. A height layer index is assigned to each height layer. The axial height coordinates corresponding to each height layer are calculated based on the lowest measured height coordinates and the fixed axial spacing, so that the axial spacing between any two adjacent height layers remains consistent.

[0080] On the horizontal section corresponding to each height layer, laser ranging units are arranged around the geometric origin along each polar angle direction, with the same number of units as the polar angle direction, so that the ranging beam of each laser ranging unit points from the geometric origin along the corresponding polar angle direction to the outer surface of the hollow part.

[0081] Each laser ranging unit is controlled to perform radial scanning on the surface of the hollowed-out part at its specified height layer and polar angle direction, and the distance from the geometric origin to the surface boundary is recorded as the raw ranging data to complete the scene initialization and polar domain reference system establishment.

[0082] The rotationally symmetric hollow part to be inspected is clamped onto a rotary table using a mechanical fixing device, so that the main rotation axis of the hollow part is perpendicular to the horizontal working plane. The intersection of the main rotation axis and the plane of the rotary table is set as the geometric origin, denoted as point A. ;

[0083] Establish a Cartesian coordinate system within the working plane and set points. Corresponding coordinates are , The positive direction of the axis points to the reference direction selected on site. The positive direction of the axis satisfies the right-hand rule;

[0084] Based on the Cartesian coordinate system, with points Establish a two-dimensional polar coordinate system for the pole, and set the polar angle variable of any point in the plane as denoted as . ;in, In order to be in After dividing the interval into equal parts along the polar angle direction, the first... Polar angles in the direction of each polar angle; Discrete index for polar angle direction; The total number of discrete equal divisions along the polar angle direction;

[0085] The axial distance between the lowest and highest measurement height positions of the part under test along the main rotation axis is denoted as the interval. ;in, , These are the axial coordinates of the lowest and highest measured height positions along the main rotation axis, respectively.

[0086] In the interval Internal division into There are equidistant height levels, and the height level numbers are set as follows: , No. The axial height of each height layer is: ;in, The total number of height layers discrete in the height direction; For discrete indexes of height levels; For the first The axial height coordinates corresponding to each height layer; This refers to the fixed axial spacing between two adjacent height layers;

[0087] At each height level Corresponding horizontal section settings The laser ranging unit makes the first Each laser ranging unit is along the polar angle direction Point of view ;

[0088] Each laser ranging unit performs a radial scan of the complex hollowed-out surface at its specified height level and polar angle, recording the data from point [point missing]. The distance to the boundary of the object's surface is used as the raw data for distance measurement.

[0089] The process of acquiring boundary distance measurements along the polar angle direction and at different altitude layers in the polar reference frame, and constructing a polar boundary data matrix covering each polar angle direction and altitude layer based on these boundary distance measurements, specifically includes:

[0090] At each combination position of polar angle and height layer, the corresponding laser ranging unit is controlled to perform multiple radial ranging operations according to the preset number of repetitions. The ranging result from the geometric origin to the boundary of the hollow part surface is recorded as the boundary distance measurement data of the corresponding combination position of polar angle and height layer.

[0091] For each combination position of polar angle direction and height layer, the arithmetic mean of multiple boundary distance measurement data recorded for the corresponding polar angle direction and height layer combination position is calculated to obtain the effective boundary distance of the corresponding polar angle direction and height layer combination position. The effective boundary distance is regarded as the average radial distance from the geometric origin to the boundary of the surface of the hollow part at the corresponding polar angle direction and height layer position.

[0092] Within the discrete two-dimensional domain spanned by all polar angle direction indices and height layer indices, a polar domain boundary data matrix is ​​established according to the polar angle direction index and height layer index. Each matrix cell corresponds one-to-one with a combination position of polar angle direction and height layer. The effective boundary distance of each combination position of polar angle direction and height layer is written into the corresponding matrix cell to form the discrete boundary function value in the polar domain boundary data matrix.

[0093] In each polar direction With height layer In the combination of positions, The boundary distance data obtained from repeated radial ranging measurements are as follows: , ;in, In the same polar angle direction With height layer The number of times the distance measurement is repeated at the combined location; For discrete indexes; The index in the polar direction is The height layer index is In the position, the The repeated measurements were obtained from the origin. Radial distance to the boundary of the cutout surface;

[0094] For each index pair The effective boundary distance after denoising is obtained by arithmetically averaging multiple ranging data points: ;in, The index in the polar direction is The height layer index is Based on the location The average radial distance obtained from repeated distance measurements;

[0095] Index in polar direction With height index layer index On the spanned discrete domain, the discrete boundary function is constructed as follows: ,form A dimensional polar domain boundary data matrix; where, For in the polar direction Height is At discrete positions, from the origin The radial distance to the boundary of the cut-out part surface is numerically related to... same.

[0096] The process of dividing the polar boundary data matrix into micro-element cells according to the grid of polar angle and height, obtaining the radial distance difference between adjacent positions for each micro-element cell, and constructing micro-element patch data and corresponding gradient information specifically includes:

[0097] In the polar domain boundary data matrix, on the discrete grid formed by the polar angle direction index and the height layer index, for each height layer other than the highest height layer, two adjacent polar angle directions and the corresponding polar angle direction between the corresponding height layer and the height layer above it are selected in the corresponding height layer to form a micro-element containing four discrete positions, so that each micro-element is limited by the four effective boundary distances of the same pair of polar angle directions on two adjacent height layers.

[0098] Set a fixed angle interval in the polar angle direction, set the polar angle difference between any two adjacent polar angle directions to the same angle value, and when the polar angle index reaches the maximum value, regard the polar angle direction corresponding to the maximum value of the polar angle index and the polar angle direction corresponding to the minimum value of the polar angle index as adjacent to each other, forming a periodic connection of polar angle directions.

[0099] For each micro-element, the angular gradient is calculated in the polar angle direction. The ratio of the difference between the effective boundary distances of two adjacent polar angle directions at the same height position within the same height layer to the fixed angular interval in the polar angle direction is used as the discrete gradient along the polar angle direction at the corresponding height position within the corresponding height layer.

[0100] For each micro-element, the height gradient is calculated in the height direction. The ratio of the difference between the effective boundary distances of two adjacent height layers in the same polar angle direction to the fixed axial spacing between adjacent height layers is used as the discrete gradient of the corresponding height position in the same polar angle direction along the height direction.

[0101] For each micro-element, first sum the square of the effective boundary distance, the square of the angular gradient, and the square of the product of the effective boundary distance and the height gradient within the micro-element. Take the square root of the summation result to obtain the surface scale factor of the corresponding micro-element. Then multiply the surface scale factor by the fixed angular interval in the polar direction and the fixed axial spacing in the height direction to obtain the local surface area of ​​the corresponding micro-element, forming local micro-element patch data.

[0102] In the discrete grid of polar angle direction index and height layer index, for each pair of indexes Selecting adjacent index pairs to form polar domain infinitesimal elements ;in, , ; The index in the polar direction is The height layer index is The polar-domain surface element is constructed at the location of the point, and the element is connected through four neighboring points. , , , The radial distance value is determined;

[0103] Applying a periodic condition in the polar angle direction, let: , ;

[0104] Set a fixed angular interval between two adjacent polar directions as follows: ;

[0105] For each index pair The discrete gradient in the polar direction is constructed as follows: ;in, The index in the polar direction is The height layer index is At the location, radial distance Along polar angle parameters Discrete rate of change;

[0106] For each index pair , , The discrete gradient in the height direction is constructed as follows: ;in, The index in the polar direction is The height layer index is At the location, radial distance Along height parameter Discrete rate of change;

[0107] For each infinitesimal element The corresponding local surface area is constructed as follows: ;in, To be compatible with polar-domain infinitesimal elements The corresponding local surface area.

[0108] The step of summing up the local surface areas on the mesh based on the data of each micro-element and gradient information to obtain the original total surface area of ​​the outer surface of the complex hollowed-out part specifically includes:

[0109] By calling the local micro-element patch data, the local surface area of ​​all micro-element units in the discrete grid composed of polar angle direction index and height layer index is accumulated to obtain the original total surface area of ​​the outer surface of the complex hollow part.

[0110] During the local surface accumulation process, a periodic connection relationship is adopted in the polar angle direction, and the maximum polar angle index position is regarded as adjacent to the minimum polar angle index position. In the height direction, an index range from the lowest height layer to the second to last height layer is adopted.

[0111] Using local area The original total surface area is constructed as follows: ;in, The original total surface area of ​​the outer surface of the complex hollowed-out part;

[0112] In calculating all and At that time, the periodic condition of polar angle direction is uniformly adopted: and using an index range: , .

[0113] The process of calculating the variance of multiple measurements at each measurement location, performing adjacency interpolation correction on unstable locations based on the variance distribution, updating boundary distance data, and re-acquiring the corresponding local surface area specifically includes:

[0114] For each combination of polar angle direction and height layer, read multiple boundary distance measurement data and effective boundary distance of the corresponding polar angle direction and height layer combination location. Squat the difference between each boundary distance measurement data and the corresponding effective boundary distance, sum them, and then divide by the number of distance measurement repetitions of the corresponding polar angle direction and height layer combination location to obtain the radial measurement variance of the corresponding polar angle direction and height layer combination location.

[0115] At all combinations of polar angles and all height layers, the radial measurement variances at each combination are calculated using an arithmetic mean to obtain the global average variance.

[0116] For each polar angle direction and its combination with all altitude layers except the highest altitude layer, the radial measurement variance of the corresponding polar angle direction and its combination with the global average variance is compared. When the radial measurement variance is greater than the global average variance, the effective boundary distances of two adjacent polar angle direction positions within the same altitude layer are selected, and the arithmetic mean of these two effective boundary distances is calculated. This arithmetic mean is then entered into the corresponding polar angle direction and its combination with the corresponding altitude layer as the updated boundary distance. When the radial measurement variance is not greater than the global average variance, the original effective boundary distances of the corresponding polar angle direction and its combination with the corresponding altitude layer remain unchanged.

[0117] After updating the boundary distances of all combined locations, the angular gradient and height gradient of each combined location are recalculated based on the updated boundary distance data and the boundary distances of adjacent locations. The local surface area of ​​each micro-element is then re-obtained according to the same surface area approximation calculation relationship as when calculating the gradient, forming local micro-element patch data after variance suppression.

[0118] For each index pair The measurement variance is constructed based on multiple ranging data as follows: ;in, The index in the polar direction is The height layer index is The radial measurement variance is calculated based on repeated ranging results at the given location.

[0119] In all index pairs The global average variance is calculated as follows: ;in, This is the arithmetic mean of the measurement variances across all polar directions and altitude layer locations;

[0120] To satisfy , index pairs In the polar angle direction, steps S501 and S502 are performed for interpolation correction, specifically as follows:

[0121] S501. Set the periodic adjacency relationship as follows: , ;

[0122] S502. The corrected boundary distance is calculated as follows: and use Replace the original ;in, For in position The radial distance after interpolation correction;

[0123] To satisfy , index pairs ,Keep constant;

[0124] For each index pair , , Use the updated version and adjacent indexes , Recalculate the polar angle gradient: and the gradient in the height direction: ;

[0125] And recalculate the corresponding local area as follows: .

[0126] Based on the updated boundary distance data, the distance difference between polar angle directions is analyzed at each height layer to identify hollow and solid regions. A mask matrix is ​​constructed and applied to the local surface area data to obtain the corrected local surface area at each polar angle direction and at each height layer combination location. This results in a corrected local surface area dataset containing the corrected local surface area at all combination locations, specifically including:

[0127] For each altitude layer other than the highest altitude layer, the effective boundary distance of each polar angle direction is read in the order of polar angle index within the corresponding altitude layer. For any two adjacent polar angle directions, the absolute value of the difference between the effective boundary distances of these two polar angle directions is calculated within the same altitude layer. The obtained absolute difference is used as the radial difference of the corresponding polar angle direction pair within the corresponding altitude layer. When the polar angle index reaches its maximum value, the polar angle direction corresponding to the maximum value of the polar angle index and the polar angle direction corresponding to the minimum value of the polar angle index are regarded as adjacent and participate in the radial difference calculation.

[0128] For each height layer except the highest height layer, collect the radial differences of all polar angle pairs within the corresponding height layer. Sort these radial differences in ascending order of value. When the number of radial differences is odd, select the radial difference at the middle position after sorting as the median radial difference of the corresponding height layer. When the number of radial differences is even, select the arithmetic mean of the radial differences at the two middle positions after sorting as the median radial difference of the corresponding height layer. Set the median radial difference as the cutout detection threshold of the corresponding height layer.

[0129] For each polar angle direction and the combination position of each height layer except the highest height layer, read the radial difference value related to the corresponding polar angle direction within the corresponding height layer. Compare the read radial difference value with the hollow detection threshold of the corresponding height layer. When the radial difference value is greater than the hollow detection threshold, mark the combination position of the corresponding polar angle direction and the corresponding height layer as a hollow area and assign a value of zero in the mask matrix. When the radial difference value is not greater than the hollow detection threshold, mark the combination position of the corresponding polar angle direction and the corresponding height layer as a solid surface area and assign a value of one in the mask matrix.

[0130] For each polar angle direction and the combination position of each height layer except the highest height layer, the value in the mask matrix is ​​multiplied by the local surface area corresponding to the combination position of the corresponding polar angle direction and the corresponding height layer to obtain the corrected local surface area after considering the suppression of the hollow area, and a corrected local surface area dataset containing the corrected local surface area of ​​all combination positions is constructed.

[0131] Indexing each height level Indexing in all polar directions The radial difference between two adjacent directions is calculated as follows: ;in, For the height layer index Within the layer, the first With the The absolute difference in average radial distance along each polar angle direction;

[0132] Taking into account the periodicity condition, let: ;

[0133] For each height level , will set Arranged in ascending order, the sequence is: ;in, To set After sorting by size from smallest to largest, in the height layer Middle row in Radial difference of position; The sorted position index;

[0134] Build height layer The corresponding median of radial differences is: ;in, The height layer index is The median of the radial differences within the layer;

[0135] Set the cutout detection threshold as follows: ;in, The height layer index is The radial jump threshold used for cutout detection within the layer;

[0136] For each index pair , , The mask construction function is as follows: ;in, The index in the polar direction is The height layer index is The value of the mask function at the position. Indicates the hollowed-out area. Represents the surface area of ​​a solid;

[0137] For each index pair , , The corrected local area under the mask is: ;in, For in position Consider masking The corrected local surface area.

[0138] The process of performing unit conversion and scale unification on the modified local surface area dataset, and accumulating the modified local surface areas of all micro-element units to obtain the final total surface area result of the outer surface of the complex hollowed-out part, specifically includes:

[0139] Read the modified local surface area dataset, accumulate the modified local surface area of ​​all combined positions formed by polar angle direction index and height layer index, and obtain the initial value of the total surface area of ​​the outer surface of the complex hollow part.

[0140] Based on the conversion relationship between the area unit of the measurement system and the expected output area unit, the initial value of the total surface area is converted to obtain the final total surface area result expressed in the expected output area unit, and the final total surface area result is stored or output.

[0141] Local area under the effect of masking The total surface area of ​​the complex hollowed-out part is: ;in, This represents the final surface area of ​​the complex hollowed-out part.

[0142] The step of cumulatively correcting the local surface area according to height layers to obtain the layered surface area and layered surface area ratio of each height layer forms the surface area distribution feature of the hollowed-out part along the height direction, specifically including:

[0143] For each height layer except the highest height layer, the corrected local surface area of ​​all polar angle directions within the corresponding height layer is accumulated to obtain the layered surface area of ​​the corresponding height layer. The layered surface areas of all height layers are arranged in order of height layer index to form a surface area sequence along the height direction.

[0144] If the final total surface area is greater than zero, the ratio of the layered surface area of ​​each height layer to the final total surface area is calculated to obtain the proportion of the layered surface area of ​​each height layer in the final total surface area. If the final total surface area is equal to zero, the proportion of the layered surface area of ​​all height layers is uniformly set to zero.

[0145] The final total surface area is used as the overall surface area feature of the complex hollowed-out part, and the surface area sequence in the height direction and the corresponding layered surface area ratio are used as the surface integral distribution feature of the complex hollowed-out part along the height direction, forming a quantitative characterization result of the complex hollowed-out structure.

[0146] Indexing each height level The surface area of ​​the layer corresponding to this height is calculated as follows: Forming a surface area sequence along the height direction ;in, For the height layer index height range Within, the cumulative value of the local surface area is corrected in all polar angular directions;

[0147] In satisfying At that time, the surface area ratio is calculated for each height level: ;in, For the first The surface area of ​​each height layer in the final total surface area The proportion of the total;

[0148] In satisfying At that time, all height layers Set as: ;

[0149] by As a characteristic quantity of the overall surface area of ​​complex hollowed-out parts, it is highly layered. and As a surface integral distribution feature quantity along the height direction of complex hollow parts.

[0150] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus.

[0151] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the technical principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for calculating the surface area of ​​complex hollowed-out parts using computer vision, characterized in that, include: The scene is initialized for the rotationally symmetric hollow part, and a polar reference system consisting of a plane rectangular coordinate system and a polar coordinate system is established around the main rotation axis and the geometric origin; In the polar reference frame, the boundary distance measurement results distributed along the polar angle direction and the height layer are obtained, and a polar boundary data matrix covering each polar angle direction and each height layer is constructed based on these boundary distance measurement results; In the polar domain boundary data matrix, micro-element cells are divided according to the grid of polar angle and height. The radial distance difference between adjacent positions is obtained for each micro-element cell to construct micro-element patch data and corresponding gradient information. Based on the data of each micro-element and gradient information, the local surface areas on the mesh are accumulated to obtain the original total surface area of ​​the outer surface of the complex hollow part. The variance of multiple measurements at each measurement location is calculated. Based on the variance distribution, adjacency interpolation correction is performed on unstable locations, the boundary distance data is updated, and the corresponding local surface area is reacquired. Based on the updated boundary distance data, the distance difference between polar angle directions is analyzed at each height layer to identify hollow areas and solid areas. A mask matrix is ​​constructed and applied to the local surface area data to obtain the corrected local surface area at each polar angle direction and at each height layer combination position, and a corrected local surface area dataset containing the corrected local surface area at all combination positions is formed. Unit conversion and scale unification are performed on the modified local surface area dataset, and the modified local surface area of ​​all micro-element units is accumulated to obtain the final total surface area result of the outer surface of the complex hollow part. The local surface area is cumulatively corrected according to the height layer, and the layer surface area and the layer surface area ratio of each height layer are obtained to form the surface area distribution feature of the hollow part along the height direction.

2. The method for calculating the surface area of ​​complex hollowed-out parts using computer vision as described in claim 1, characterized in that, The process of initializing the scene for the rotationally symmetric hollowed-out component, and establishing a polar reference system composed of a Cartesian coordinate system and a polar coordinate system around the main rotation axis and the geometric origin, specifically includes: The rotationally symmetric hollow part to be inspected is clamped on the rotary worktable by a mechanical fixing device, so that the main rotation axis of the hollow part is kept vertical and orthogonal to the horizontal working plane, and the intersection of the main rotation axis and the plane of the rotary worktable is set as the geometric origin. Establish a Cartesian coordinate system in the horizontal working plane, set the coordinates of the geometric origin in the Cartesian coordinate system as the zero point coordinates, point the positive direction of the first coordinate axis to the reference direction selected on site, and set the positive direction of the second coordinate axis relative to the first coordinate axis according to the right-hand rule. Based on the Cartesian coordinate system, a two-dimensional polar coordinate system is established with the geometric origin as the pole. Multiple polar directions are divided within a circumference angle according to the same angular interval. Discrete indices are assigned to each polar direction, and the correspondence between each polar direction and the Cartesian coordinate system is recorded. The lowest and highest measurement height positions of the part under test are obtained along the main rotation axis, forming an axial measurement interval between them, and the coordinates of the lowest and highest measurement heights are recorded respectively. Within the axial measurement range, multiple height layers are divided according to the same axial spacing. A height layer index is assigned to each height layer. The axial height coordinates corresponding to each height layer are calculated based on the lowest measured height coordinates and the fixed axial spacing, so that the axial spacing between any two adjacent height layers remains consistent. On the horizontal section corresponding to each height layer, laser ranging units are arranged around the geometric origin along each polar angle direction, with the same number of units as the polar angle direction, so that the ranging beam of each laser ranging unit points from the geometric origin along the corresponding polar angle direction to the outer surface of the hollow part. Each laser ranging unit is controlled to perform radial scanning on the surface of the hollowed-out part at its specified height layer and polar angle direction, and the distance from the geometric origin to the surface boundary is recorded as the raw ranging data to complete the scene initialization and polar domain reference system establishment.

3. The method for calculating the surface area of ​​complex hollowed-out parts using computer vision as described in claim 2, characterized in that, The process of acquiring boundary distance measurements along the polar angle direction and at different altitude layers in the polar reference frame, and constructing a polar boundary data matrix covering each polar angle direction and altitude layer based on these boundary distance measurements, specifically includes: At each combination position of polar angle and height layer, the corresponding laser ranging unit is controlled to perform multiple radial ranging operations according to the preset number of repetitions. The ranging result from the geometric origin to the boundary of the hollow part surface is recorded as the boundary distance measurement data of the corresponding combination position of polar angle and height layer. For each combination position of polar angle direction and height layer, the arithmetic mean of multiple boundary distance measurement data recorded for the corresponding polar angle direction and height layer combination position is calculated to obtain the effective boundary distance of the corresponding polar angle direction and height layer combination position. The effective boundary distance is regarded as the average radial distance from the geometric origin to the boundary of the surface of the hollow part at the corresponding polar angle direction and height layer position. Within the discrete two-dimensional domain spanned by all polar angle direction indices and height layer indices, a polar domain boundary data matrix is ​​established according to the polar angle direction index and height layer index. Each matrix cell corresponds one-to-one with a combination position of polar angle direction and height layer. The effective boundary distance of each combination position of polar angle direction and height layer is written into the corresponding matrix cell to form the discrete boundary function value in the polar domain boundary data matrix.

4. The method for calculating the surface area of ​​complex hollowed-out parts using computer vision as described in claim 3, characterized in that, The process of dividing the polar boundary data matrix into micro-element cells according to the grid of polar angle and height, obtaining the radial distance difference between adjacent positions for each micro-element cell, and constructing micro-element patch data and corresponding gradient information specifically includes: In the polar domain boundary data matrix, on the discrete grid formed by the polar angle direction index and the height layer index, for each height layer other than the highest height layer, two adjacent polar angle directions and the corresponding polar angle direction between the corresponding height layer and the height layer above it are selected in the corresponding height layer to form a micro-element containing four discrete positions, so that each micro-element is limited by the four effective boundary distances of the same pair of polar angle directions on two adjacent height layers. Set a fixed angle interval in the polar angle direction, set the polar angle difference between any two adjacent polar angle directions to the same angle value, and when the polar angle index reaches the maximum value, regard the polar angle direction corresponding to the maximum value of the polar angle index and the polar angle direction corresponding to the minimum value of the polar angle index as adjacent to each other, forming a periodic connection of polar angle directions. For each micro-element, the angular gradient is calculated in the polar angle direction. The ratio of the difference between the effective boundary distances of two adjacent polar angle directions at the same height position within the same height layer to the fixed angular interval in the polar angle direction is used as the discrete gradient along the polar angle direction at the corresponding height position within the corresponding height layer. For each micro-element, the height gradient is calculated in the height direction. The ratio of the difference between the effective boundary distances of two adjacent height layers in the same polar angle direction to the fixed axial spacing between adjacent height layers is used as the discrete gradient of the corresponding height position in the same polar angle direction along the height direction. For each micro-element, first sum the square of the effective boundary distance, the square of the angular gradient, and the square of the product of the effective boundary distance and the height gradient within the micro-element. Take the square root of the summation result to obtain the surface scale factor of the corresponding micro-element. Then multiply the surface scale factor by the fixed angular interval in the polar direction and the fixed axial spacing in the height direction to obtain the local surface area of ​​the corresponding micro-element, forming local micro-element patch data.

5. The method for calculating the surface area of ​​complex hollowed-out parts using computer vision as described in claim 4, characterized in that, The step of summing up the local surface areas on the mesh based on the data of each micro-element and gradient information to obtain the original total surface area of ​​the outer surface of the complex hollowed-out part specifically includes: By calling the local micro-element patch data, the local surface area of ​​all micro-element units in the discrete grid composed of polar angle direction index and height layer index is accumulated to obtain the original total surface area of ​​the outer surface of the complex hollow part. During the local surface accumulation process, a periodic connection relationship is adopted in the polar angle direction, and the maximum polar angle index position is regarded as adjacent to the minimum polar angle index position. In the height direction, an index range from the lowest height layer to the second to last height layer is adopted.

6. The method for calculating the surface area of ​​complex hollowed-out parts using computer vision as described in claim 5, characterized in that, The process of calculating the variance of multiple measurements at each measurement location, performing adjacency interpolation correction on unstable locations based on the variance distribution, updating boundary distance data, and re-acquiring the corresponding local surface area specifically includes: For each combination of polar angle direction and height layer, read multiple boundary distance measurement data and effective boundary distance of the corresponding polar angle direction and height layer combination location. Squat the difference between each boundary distance measurement data and the corresponding effective boundary distance, sum them, and then divide by the number of distance measurement repetitions of the corresponding polar angle direction and height layer combination location to obtain the radial measurement variance of the corresponding polar angle direction and height layer combination location. At all combinations of polar angles and all height layers, the radial measurement variances at each combination are calculated using an arithmetic mean to obtain the global average variance. For each polar angle direction and its combination with all altitude layers except the highest altitude layer, the radial measurement variance of the corresponding polar angle direction and its combination with the global average variance is compared. When the radial measurement variance is greater than the global average variance, the effective boundary distances of two adjacent polar angle direction positions within the same altitude layer are selected, and the arithmetic mean of these two effective boundary distances is calculated. This arithmetic mean is then entered into the corresponding polar angle direction and its combination with the corresponding altitude layer as the updated boundary distance. When the radial measurement variance is not greater than the global average variance, the original effective boundary distances of the corresponding polar angle direction and its combination with the corresponding altitude layer remain unchanged. After updating the boundary distances of all combined locations, the angular gradient and height gradient of each combined location are recalculated based on the updated boundary distance data and the boundary distances of adjacent locations. The local surface area of ​​each micro-element is then re-obtained according to the same surface area approximation calculation relationship as when calculating the gradient, forming local micro-element patch data after variance suppression.

7. The method for calculating the surface area of ​​complex hollowed-out parts using computer vision as described in claim 6, characterized in that, Based on the updated boundary distance data, the distance difference between polar angle directions is analyzed at each height layer to identify hollow and solid regions. A mask matrix is ​​constructed and applied to the local surface area data to obtain the corrected local surface area at each polar angle direction and at each height layer combination location. This results in a corrected local surface area dataset containing the corrected local surface area at all combination locations, specifically including: For each altitude layer other than the highest altitude layer, the effective boundary distance of each polar angle direction is read in the order of polar angle index within the corresponding altitude layer. For any two adjacent polar angle directions, the absolute value of the difference between the effective boundary distances of these two polar angle directions is calculated within the same altitude layer. The obtained absolute difference is used as the radial difference of the corresponding polar angle direction pair within the corresponding altitude layer. When the polar angle index reaches its maximum value, the polar angle direction corresponding to the maximum value of the polar angle index and the polar angle direction corresponding to the minimum value of the polar angle index are regarded as adjacent and participate in the radial difference calculation. For each height layer except the highest height layer, collect the radial differences of all polar angle pairs within the corresponding height layer. Sort these radial differences in ascending order of value. When the number of radial differences is odd, select the radial difference at the middle position after sorting as the median radial difference of the corresponding height layer. When the number of radial differences is even, select the arithmetic mean of the radial differences at the two middle positions after sorting as the median radial difference of the corresponding height layer. Set the median radial difference as the cutout detection threshold of the corresponding height layer. For each polar angle direction and the combination position of each height layer except the highest height layer, read the radial difference value related to the corresponding polar angle direction within the corresponding height layer. Compare the read radial difference value with the hollow detection threshold of the corresponding height layer. When the radial difference value is greater than the hollow detection threshold, mark the combination position of the corresponding polar angle direction and the corresponding height layer as a hollow area and assign a value of zero in the mask matrix. When the radial difference value is not greater than the hollow detection threshold, mark the combination position of the corresponding polar angle direction and the corresponding height layer as a solid surface area and assign a value of one in the mask matrix. For each polar angle direction and the combination position of each height layer except the highest height layer, the value in the mask matrix is ​​multiplied by the local surface area corresponding to the combination position of the corresponding polar angle direction and the corresponding height layer to obtain the corrected local surface area after considering the suppression of the hollow area, and a corrected local surface area dataset containing the corrected local surface area of ​​all combination positions is constructed.

8. The method for calculating the surface area of ​​complex hollowed-out parts using computer vision as described in claim 7, characterized in that, The process of performing unit conversion and scale unification on the modified local surface area dataset, and accumulating the modified local surface areas of all micro-element units to obtain the final total surface area result of the outer surface of the complex hollowed-out part, specifically includes: Read the modified local surface area dataset, accumulate the modified local surface area of ​​all combined positions formed by polar angle direction index and height layer index, and obtain the initial value of the total surface area of ​​the outer surface of the complex hollow part. Based on the conversion relationship between the area unit of the measurement system and the expected output area unit, the initial value of the total surface area is converted to obtain the final total surface area result expressed in the expected output area unit, and the final total surface area result is stored or output.

9. The method for calculating the surface area of ​​complex hollowed-out parts using computer vision as described in claim 8, characterized in that, The step of cumulatively correcting the local surface area according to height layers to obtain the layered surface area and layered surface area ratio of each height layer forms the surface area distribution feature of the hollowed-out part along the height direction, specifically including: For each height layer except the highest height layer, the corrected local surface area of ​​all polar angle directions within the corresponding height layer is accumulated to obtain the layered surface area of ​​the corresponding height layer. The layered surface areas of all height layers are arranged in order of height layer index to form a surface area sequence along the height direction. If the final total surface area is greater than zero, the ratio of the layered surface area of ​​each height layer to the final total surface area is calculated to obtain the proportion of the layered surface area of ​​each height layer in the final total surface area. If the final total surface area is equal to zero, the proportion of the layered surface area of ​​all height layers is uniformly set to zero. The final total surface area is used as the overall surface area feature of the complex hollowed-out part, and the surface area sequence in the height direction and the corresponding layered surface area ratio are used as the surface integral distribution feature of the complex hollowed-out part along the height direction, forming a quantitative characterization result of the complex hollowed-out structure.

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